Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which expression is equivalent to 
4^(-4)×(4^(-2))/(4^(2))?

4^(16)

16^(16)

16^(-8)

4^(-8)

Which expression is equivalent to 44×4242? 4^{-4} \times \frac{4^{-2}}{4^{2}} ? \newline416 4^{16} \newline1616 16^{16} \newline168 16^{-8} \newline48 4^{-8}

Full solution

Q. Which expression is equivalent to 44×4242? 4^{-4} \times \frac{4^{-2}}{4^{2}} ? \newline416 4^{16} \newline1616 16^{16} \newline168 16^{-8} \newline48 4^{-8}
  1. Apply Properties of Exponents: Simplify the expression using the properties of exponents.\newlineWe have the expression 44×(42)/(42)4^{-4}\times(4^{-2})/(4^{2}). According to the properties of exponents, when we multiply powers with the same base, we add the exponents, and when we divide powers with the same base, we subtract the exponents.
  2. Combine Exponents in Numerator: Combine the exponents in the numerator.\newlineWe have 44×424^{-4}\times4^{-2}, which can be combined as 4(4+2)4^{(-4 + -2)} because we add the exponents when multiplying with the same base.\newline44×42=4(4+2)=46.4^{-4}\times4^{-2} = 4^{(-4 + -2)} = 4^{-6}.
  3. Divide Numerator by Denominator: Divide the numerator by the denominator.\newlineNow we have 46/424^{-6} / 4^{2}. According to the properties of exponents, when we divide powers with the same base, we subtract the exponents.\newline46/42=462=484^{-6} / 4^{2} = 4^{-6 - 2} = 4^{-8}.
  4. Check Answer Choices: Check the answer choices to see which one matches our result.\newlineWe have found that the expression simplifies to 484^{-8}. Looking at the answer choices, we see that the equivalent expression is 484^{-8}.

More problems from Operations with rational exponents